[1]} observe that, when the model is non-convex and misspecified, there is a chance for hyper-compression. This is the term they use to describe the seemingly paradoxical result that the Bayesian predictive distribution can be closer, in a Kullback–Leibler sense, to the true \(P^\star \)  then the within-model Kullback–Leibler minimizer \(P_{\theta ^\dagger }\) . What makes this possible is non-convexity: the predictive distribution is an average of in-model distributions \(P_\theta \)  which, without convexity, could end up outside the model and potentially closer to \(P^\star \)  than is \(P_{\theta ^\dagger }\) . Besides being counter-intuitive, hyper-compression also reveals a practical problem, namely, inconsistency—that the posterior distribution is not concentrating its mass near \(\theta ^\dagger \)  as expected. To overcome this, [1]} suggest to work with a new (hypothetical) model, with densities
\( p_\theta ^{(\eta )}(x,y) = p^\star (x,y) \bigl \lbrace  p_\theta (y \mid x) / p_{\theta ^\dagger }(y \mid x) \bigr \rbrace ^\eta , \) 
